Trigonometric Inequalities

Geometry Level 2

If a triangle has internal angles A, B, and C, none of which exceeds 90°.

Then the following inequalities are true.

sin A + sin B + sin C > p

cos A + cos B + cos C > q

tan (A/2) + tan (B/2) + tan (C/2) < r

Where p, q and r are all integers > 0

Find p + q + r

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